// EvalFunc evaluates a function on every window in an image.
// If the input image is M x N and the window size is m x n,
// then the output is (M-m+1) x (N-n+1).
// If the window size is larger than the image size in either dimension,
// a nil image is returned with no error.
func EvalFunc(im *rimg64.Multi, size image.Point, f ScoreFunc) (*rimg64.Image, error) {
if im.Width < size.X || im.Height < size.Y {
return nil, nil
}
r := rimg64.New(im.Width-size.X+1, im.Height-size.Y+1)
x := rimg64.NewMulti(size.X, size.Y, im.Channels)
for i := 0; i < r.Width; i++ {
for j := 0; j < r.Height; j++ {
// Copy window into x.
for u := 0; u < size.X; u++ {
for v := 0; v < size.Y; v++ {
for p := 0; p < im.Channels; p++ {
x.Set(u, v, p, im.At(i+u, j+v, p))
}
}
}
y, err := f(x)
if err != nil {
return nil, err
}
r.Set(i, j, y)
}
}
return r, nil
}
// CorrMultiBankFFT computes the correlation of
// a multi-channel image with a multi-channel filter.
// h[u, v] = sum_p (f_p corr g_p)[u, v]
func CorrMultiFFT(f, g *rimg64.Multi) (*rimg64.Image, error) {
if err := errIfChannelsNotEq(f, g); err != nil {
panic(err)
}
out := ValidSize(f.Size(), g.Size())
if out.Eq(image.ZP) {
return nil, nil
}
work, _ := FFT2Size(f.Size())
fhat := fftw.NewArray2(work.X, work.Y)
ghat := fftw.NewArray2(work.X, work.Y)
ffwd := fftw.NewPlan2(fhat, fhat, fftw.Forward, fftw.Estimate)
defer ffwd.Destroy()
gfwd := fftw.NewPlan2(ghat, ghat, fftw.Forward, fftw.Estimate)
defer gfwd.Destroy()
hhat := fftw.NewArray2(work.X, work.Y)
for p := 0; p < f.Channels; p++ {
// Take transform of each channel.
copyChannelTo(fhat, f, p)
ffwd.Execute()
copyChannelTo(ghat, g, p)
gfwd.Execute()
addMul(hhat, ghat, fhat)
}
n := float64(work.X * work.Y)
scale(complex(1/n, 0), hhat)
fftw.IFFT2To(hhat, hhat)
h := rimg64.New(out.X, out.Y)
copyRealTo(h, hhat)
return h, nil
}
func randImage(width, height int) *rimg64.Image {
f := rimg64.New(width, height)
for i := 0; i < width; i++ {
for j := 0; j < height; j++ {
f.Set(i, j, rand.NormFloat64())
}
}
return f
}
// Flip mirrors an image in x and y.
func Flip(f *rimg64.Image) *rimg64.Image {
g := rimg64.New(f.Width, f.Height)
for i := 0; i < f.Width; i++ {
for j := 0; j < f.Height; j++ {
g.Set(f.Width-1-i, f.Height-1-j, f.At(i, j))
}
}
return g
}
func square(f *rimg64.Image) *rimg64.Image {
g := rimg64.New(f.Width, f.Height)
for i := 0; i < f.Width; i++ {
for j := 0; j < f.Height; j++ {
g.Set(i, j, sqr(f.At(i, j)))
}
}
return g
}
// CorrMultiStrideBLAS computes the strided correlation of
// a multi-channel image with a multi-channel filter.
// h[u, v] = sum_q (f_q corr g_q)[stride*u, stride*v]
func CorrMultiStrideBLAS(f, g *rimg64.Multi, stride int) (*rimg64.Image, error) {
out := ValidSizeStride(f.Size(), g.Size(), stride)
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
h := rimg64.New(out.X, out.Y)
// Size of filters.
m, n, k := g.Width, g.Height, g.Channels
// Express as dense matrix multiplication.
// h[u, v] = sum_q (f_q corr g_q)[stride*u, stride*v]
// y(h) = A(f) x(g)
// where A is wh by mnk
// with w = ceil[(M-m+1)/stride],
// h = ceil[(N-n+1)/stride].
a := blas.NewMat(h.Width*h.Height, m*n*k)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
var s int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for q := 0; q < g.Channels; q++ {
a.Set(r, s, f.At(stride*u+i, stride*v+j, q))
s++
}
}
}
r++
}
}
}
x := blas.NewMat(m*n*k, 1)
{
var r int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
for q := 0; q < g.Channels; q++ {
x.Set(r, 0, g.At(i, j, q))
r++
}
}
}
}
y := blas.MatMul(1, a, x)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
h.Set(u, v, y.At(r, 0))
r++
}
}
}
return h, nil
}
// Decimate takes every r-th sample starting at (0, 0).
func Decimate(f *rimg64.Image, r int) *rimg64.Image {
out := ceilDivPt(f.Size(), r)
g := rimg64.New(out.X, out.Y)
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
g.Set(i, j, f.At(r*i, r*j))
}
}
return g
}
// CorrMultiStrideFFT computes the correlation of
// a multi-channel image with a multi-channel filter.
// h[u, v] = sum_q (f_q corr g_q)[u, v]
func CorrMultiStrideFFT(f, g *rimg64.Multi, stride int) (*rimg64.Image, error) {
if err := errIfChannelsNotEq(f, g); err != nil {
panic(err)
}
out := ValidSizeStride(f.Size(), g.Size(), stride)
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
// Compute strided convolution as the sum over
// a stride x stride grid of small convolutions.
grid := image.Pt(stride, stride)
// But do not divide into a larger grid than the size of the filter.
// If the filter is smaller than the stride,
// then some pixels in the image will not affect the output.
grid.X = min(grid.X, g.Width)
grid.Y = min(grid.Y, g.Height)
// Determine the size of the sub-sampled filter.
gsub := image.Pt(ceilDiv(g.Width, grid.X), ceilDiv(g.Height, grid.Y))
// The sub-sampled size of the image should be such that
// the output size is attained.
fsub := image.Pt(out.X+gsub.X-1, out.Y+gsub.Y-1)
// Determine optimal size for FFT.
work, _ := FFT2Size(fsub)
// Cache FFT of each channel of image for convolving with multiple filters.
// Re-use plan for multiple convolutions too.
fhat := fftw.NewArray2(work.X, work.Y)
ffwd := fftw.NewPlan2(fhat, fhat, fftw.Forward, fftw.Estimate)
defer ffwd.Destroy()
ghat := fftw.NewArray2(work.X, work.Y)
gfwd := fftw.NewPlan2(ghat, ghat, fftw.Forward, fftw.Estimate)
defer gfwd.Destroy()
// Normalization factor.
alpha := complex(1/float64(work.X*work.Y), 0)
// Add the convolutions over channels and strides.
hhat := fftw.NewArray2(work.X, work.Y)
for k := 0; k < f.Channels; k++ {
for i := 0; i < grid.X; i++ {
for j := 0; j < grid.Y; j++ {
// Copy each downsampled channel and take its transform.
copyChannelStrideTo(fhat, f, k, stride, image.Pt(i, j))
ffwd.Execute()
copyChannelStrideTo(ghat, g, k, stride, image.Pt(i, j))
gfwd.Execute()
addMul(hhat, ghat, fhat)
}
}
}
// Take the inverse transform.
h := rimg64.New(out.X, out.Y)
scale(alpha, hhat)
fftw.IFFT2To(hhat, hhat)
copyRealTo(h, hhat)
return h, nil
}
// Takes the sum over channels.
func squareMulti(f *rimg64.Multi) *rimg64.Image {
g := rimg64.New(f.Width, f.Height)
for i := 0; i < f.Width; i++ {
for j := 0; j < f.Height; j++ {
for k := 0; k < f.Channels; k++ {
g.Set(i, j, g.At(i, j)+sqr(f.At(i, j, k)))
}
}
}
return g
}
// CorrBLAS computes the correlation of an image with a filter.
// h[u, v] = (f corr g)[u, v]
func CorrBLAS(f, g *rimg64.Image) (*rimg64.Image, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
h := rimg64.New(out.X, out.Y)
// Size of filters.
m, n := g.Width, g.Height
// Express as dense matrix multiplication.
// h[u, v] = (f corr g)[u, v]
// y(h) = A(f) x(g)
// where A is (M-m+1)(N-n+1) by mn.
a := blas.NewMat(h.Width*h.Height, m*n)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
var s int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
a.Set(r, s, f.At(u+i, v+j))
s++
}
}
r++
}
}
}
x := blas.NewMat(m*n, 1)
{
var r int
for i := 0; i < g.Width; i++ {
for j := 0; j < g.Height; j++ {
x.Set(r, 0, g.At(i, j))
r++
}
}
}
y := blas.MatMul(1, a, x)
{
var r int
for u := 0; u < h.Width; u++ {
for v := 0; v < h.Height; v++ {
h.Set(u, v, y.At(r, 0))
r++
}
}
}
return h, nil
}
// CorrStrideNaive computes the strided correlation of an image with a filter.
// h[u, v] = (f corr g)[stride*u, stride*v]
func CorrStrideNaive(f, g *rimg64.Image, stride int) (*rimg64.Image, error) {
out := ValidSizeStride(f.Size(), g.Size(), stride)
h := rimg64.New(out.X, out.Y)
for i := 0; i < h.Width; i++ {
for j := 0; j < h.Height; j++ {
var total float64
for u := 0; u < g.Width; u++ {
for v := 0; v < g.Height; v++ {
p := image.Pt(i, j).Mul(stride).Add(image.Pt(u, v))
total += f.At(p.X, p.Y) * g.At(u, v)
}
}
h.Set(i, j, total)
}
}
return h, nil
}
// CorrNaive computes the correlation of an image with a filter.
// h[u, v] = (f corr g)[u, v]
func CorrNaive(f, g *rimg64.Image) (*rimg64.Image, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
h := rimg64.New(out.X, out.Y)
for i := 0; i < out.X; i++ {
for j := 0; j < out.Y; j++ {
var total float64
for u := 0; u < g.Width; u++ {
for v := 0; v < g.Height; v++ {
total += f.At(i+u, j+v) * g.At(u, v)
}
}
h.Set(i, j, total)
}
}
return h, nil
}
// CorrMultiStrideNaive computes the correlation of
// a multi-channel image with a multi-channel filter.
// h[u, v] = sum_q (f_q corr g_q)[u, v]
func CorrMultiStrideNaive(f, g *rimg64.Multi, stride int) (*rimg64.Image, error) {
if err := errIfChannelsNotEq(f, g); err != nil {
panic(err)
}
out := ValidSizeStride(f.Size(), g.Size(), stride)
h := rimg64.New(out.X, out.Y)
for i := 0; i < h.Width; i++ {
for j := 0; j < h.Height; j++ {
var total float64
for u := 0; u < g.Width; u++ {
for v := 0; v < g.Height; v++ {
p := image.Pt(i, j).Mul(stride).Add(image.Pt(u, v))
for k := 0; k < f.Channels; k++ {
total += f.At(p.X, p.Y, k) * g.At(u, v, k)
}
}
}
h.Set(i, j, total)
}
}
return h, nil
}
// CorrFFT computes the correlation of an image with a filter.
// h[u, v] = (f corr g)[u, v]
func CorrFFT(f, g *rimg64.Image) (*rimg64.Image, error) {
out := ValidSize(f.Size(), g.Size())
if out.X <= 0 || out.Y <= 0 {
return nil, nil
}
// Determine optimal size for FFT.
work, _ := FFT2Size(f.Size())
fhat := fftw.NewArray2(work.X, work.Y)
ghat := fftw.NewArray2(work.X, work.Y)
// Take forward transforms.
copyImageTo(fhat, f)
fftw.FFT2To(fhat, fhat)
copyImageTo(ghat, g)
fftw.FFT2To(ghat, ghat)
// Scale such that convolution theorem holds.
n := float64(work.X * work.Y)
scaleMul(fhat, complex(1/n, 0), ghat, fhat)
// Take inverse transform.
h := rimg64.New(out.X, out.Y)
fftw.IFFT2To(fhat, fhat)
copyRealTo(h, fhat)
return h, nil
}
// Explicitly forms vectors and computes normalized dot product.
func cosCorrMultiNaive(f, g *rimg64.Multi) *rimg64.Image {
h := rimg64.New(f.Width-g.Width+1, f.Height-g.Height+1)
n := g.Width * g.Height * g.Channels
a := make([]float64, n)
b := make([]float64, n)
for i := 0; i < h.Width; i++ {
for j := 0; j < h.Height; j++ {
a = a[:0]
b = b[:0]
for u := 0; u < g.Width; u++ {
for v := 0; v < g.Height; v++ {
for p := 0; p < g.Channels; p++ {
a = append(a, f.At(i+u, j+v, p))
b = append(b, g.At(u, v, p))
}
}
}
floats.Scale(1/floats.Norm(a, 2), a)
floats.Scale(1/floats.Norm(b, 2), b)
h.Set(i, j, floats.Dot(a, b))
}
}
return h
}
// CorrMultiNaive computes the correlation of
// a multi-channel image with a multi-channel filter.
// h[u, v] = sum_p (f_p corr g_p)[u, v]
func CorrMultiNaive(f, g *rimg64.Multi) (*rimg64.Image, error) {
if err := errIfChannelsNotEq(f, g); err != nil {
panic(err)
}
out := ValidSize(f.Size(), g.Size())
if out.Eq(image.ZP) {
return nil, nil
}
h := rimg64.New(out.X, out.Y)
for i := 0; i < out.X; i++ {
for j := 0; j < out.Y; j++ {
var total float64
for u := 0; u < g.Width; u++ {
for v := 0; v < g.Height; v++ {
for p := 0; p < f.Channels; p++ {
total += f.At(i+u, j+v, p) * g.At(u, v, p)
}
}
}
h.Set(i, j, total)
}
}
return h, nil
}
func HOG(f *rimg64.Multi, conf Config) *rimg64.Multi {
const eps = 0.0001
// Leave a one-pixel border to compute derivatives.
inside := image.Rectangle{image.ZP, f.Size()}.Inset(1)
// Leave a half-cell border.
half := conf.CellSize / 2
valid := inside.Inset(half)
// Number of whole cells inside valid region.
cells := valid.Size().Div(conf.CellSize)
if cells.X <= 0 || cells.Y <= 0 {
return nil
}
// Remove one cell on all sides for output.
out := cells.Sub(image.Pt(2, 2))
// Region to iterate over.
size := cells.Mul(conf.CellSize).Add(image.Pt(2*half, 2*half))
vis := image.Rectangle{inside.Min, inside.Min.Add(size)}
// Accumulate edges into cell histograms.
hist := rimg64.NewMulti(cells.X, cells.Y, 2*conf.Angles)
quantizer := makeQuantizer(conf.Angles)
for a := vis.Min.X; a < vis.Max.X; a++ {
for b := vis.Min.Y; b < vis.Max.Y; b++ {
x, y := a-half-vis.Min.X, b-half-vis.Min.Y
// Pick channel with strongest gradient.
grad, v := maxGrad(f, a, b)
v = math.Sqrt(v)
// Snap to orientation.
q := quantizer.quantize(grad)
// Add to 4 histograms around pixel using bilinear interpolation.
xp := (float64(x)+0.5)/float64(conf.CellSize) - 0.5
yp := (float64(y)+0.5)/float64(conf.CellSize) - 0.5
// Extract integer and fractional part.
ixp, vx0 := modf(xp)
iyp, vy0 := modf(yp)
// Complement of fraction part.
vx1 := 1 - vx0
vy1 := 1 - vy0
if ixp >= 0 && iyp >= 0 {
addToMulti(hist, ixp, iyp, q, vx1*vy1*v)
}
if ixp+1 < cells.X && iyp >= 0 {
addToMulti(hist, ixp+1, iyp, q, vx0*vy1*v)
}
if ixp >= 0 && iyp+1 < cells.Y {
addToMulti(hist, ixp, iyp+1, q, vx1*vy0*v)
}
if ixp+1 < cells.X && iyp+1 < cells.Y {
addToMulti(hist, ixp+1, iyp+1, q, vx0*vy0*v)
}
}
}
// compute energy in each block by summing over orientations
norm := rimg64.New(cells.X, cells.Y)
for x := 0; x < cells.X; x++ {
for y := 0; y < cells.Y; y++ {
for d := 0; d < conf.Angles; d++ {
s := hist.At(x, y, d) + hist.At(x, y, d+conf.Angles)
addTo(norm, x, y, s*s)
}
}
}
feat := rimg64.NewMulti(out.X, out.Y, conf.Channels())
for x := 0; x < out.X; x++ {
for y := 0; y < out.Y; y++ {
a, b := x+1, y+1
// Normalization factors.
var n [4]float64
n[0] = 1 / math.Sqrt(adjSum(norm, a, b, a+1, b+1)+eps)
n[1] = 1 / math.Sqrt(adjSum(norm, a, b, a+1, b-1)+eps)
n[2] = 1 / math.Sqrt(adjSum(norm, a, b, a-1, b+1)+eps)
n[3] = 1 / math.Sqrt(adjSum(norm, a, b, a-1, b-1)+eps)
var off int
// Contrast-sensitive features.
if !conf.NoContrastVar {
for d := 0; d < 2*conf.Angles; d++ {
h := hist.At(a, b, d)
var sum float64
for _, ni := range n {
val := h * ni
if !conf.NoClip {
val = math.Min(val, 0.2)
}
sum += val
}
feat.Set(x, y, off+d, sum/2)
}
off += 2 * conf.Angles
}
// Contrast-insensitive features.
if !conf.NoContrastInvar {
for d := 0; d < conf.Angles; d++ {
h := hist.At(a, b, d) + hist.At(a, b, conf.Angles+d)
var sum float64
for _, ni := range n {
val := h * ni
if !conf.NoClip {
val = math.Min(val, 0.2)
}
sum += val
}
feat.Set(x, y, off+d, sum/2)
}
off += conf.Angles
}
// Texture features.
if !conf.NoTexture {
for i, ni := range n {
var sum float64
for d := 0; d < 2*conf.Angles; d++ {
h := hist.At(a, b, d)
val := h * ni
if !conf.NoClip {
val = math.Min(val, 0.2)
}
sum += val
}
feat.Set(x, y, off+i, sum/math.Sqrt(float64(2*conf.Angles)))
}
off += 4
}
}
}
return feat
}
